635FinalProject

library(tidyverse)

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library(corrplot)

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library("PerformanceAnalytics")

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library(gtsummary)

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library(flextable)

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library(caret)

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library(glmnet)

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library(e1071)

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food_data <- read_csv("Food_Supply_kcal_Data.csv")

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## ── Column specification ────────────────────────────────────────────────────────
## cols(
##   .default = col_double(),
##   Country = col_character(),
##   Undernourished = col_character(),
##   `Unit (all except Population)` = col_character()
## )
## ℹ Use `spec()` for the full column specifications.

head(food_data)

## # A tibble: 6 x 32
##   Country `Alcoholic Beve… `Animal Product… `Animal fats` `Aquatic Produc…
##   <chr>              <dbl>            <dbl>         <dbl>            <dbl>
## 1 Afghan…           0                  4.78         0.850                0
## 2 Albania           0.912             16.1          1.06                 0
## 3 Algeria           0.0896             6.03         0.194                0
## 4 Angola            1.94               4.69         0.264                0
## 5 Antigu…           2.30              15.4          1.54                 0
## 6 Argent…           1.44              15.0          1.06                 0
## # … with 27 more variables: `Cereals - Excluding Beer` <dbl>, Eggs <dbl>,
## #   `Fish, Seafood` <dbl>, `Fruits - Excluding Wine` <dbl>, Meat <dbl>, `Milk -
## #   Excluding Butter` <dbl>, Miscellaneous <dbl>, Offals <dbl>, Oilcrops <dbl>,
## #   Pulses <dbl>, Spices <dbl>, `Starchy Roots` <dbl>, Stimulants <dbl>, `Sugar
## #   Crops` <dbl>, `Sugar & Sweeteners` <dbl>, Treenuts <dbl>, `Vegetal
## #   Products` <dbl>, `Vegetable Oils` <dbl>, Vegetables <dbl>, Obesity <dbl>,
## #   Undernourished <chr>, Confirmed <dbl>, Deaths <dbl>, Recovered <dbl>,
## #   Active <dbl>, Population <dbl>, `Unit (all except Population)` <chr>

sum(food_data[1,2:24])

## [1] 100.0002

food_data <- food_data  %>%
  drop_na() %>%
  mutate(Confirmed_per_capita = Confirmed/Population * 100000000, Deaths_per_capita = Deaths/Population * 100000000) %>%
  #creating a column that specifies whether each country falls above or below the median
  mutate(Cases_vs_median = as.character(ifelse(Confirmed_per_capita > median(Confirmed_per_capita), "Above", "Below")), 
         Deaths_vs_median = as.character(ifelse(Deaths_per_capita > median(Deaths_per_capita), "Above", "Below")))

food_data <- food_data %>%
  select(-Miscellaneous, -Obesity, -Undernourished, -Recovered, -Active, -Population, -`Unit (all except Population)`, 
         -Confirmed, -Deaths)
head(food_data)

## # A tibble: 6 x 27
##   Country `Alcoholic Beve… `Animal Product… `Animal fats` `Aquatic Produc…
##   <chr>              <dbl>            <dbl>         <dbl>            <dbl>
## 1 Afghan…           0                  4.78         0.850                0
## 2 Albania           0.912             16.1          1.06                 0
## 3 Algeria           0.0896             6.03         0.194                0
## 4 Angola            1.94               4.69         0.264                0
## 5 Argent…           1.44              15.0          1.06                 0
## 6 Armenia           0.227             12.8          1.77                 0
## # … with 22 more variables: `Cereals - Excluding Beer` <dbl>, Eggs <dbl>,
## #   `Fish, Seafood` <dbl>, `Fruits - Excluding Wine` <dbl>, Meat <dbl>, `Milk -
## #   Excluding Butter` <dbl>, Offals <dbl>, Oilcrops <dbl>, Pulses <dbl>,
## #   Spices <dbl>, `Starchy Roots` <dbl>, Stimulants <dbl>, `Sugar Crops` <dbl>,
## #   `Sugar & Sweeteners` <dbl>, Treenuts <dbl>, `Vegetal Products` <dbl>,
## #   `Vegetable Oils` <dbl>, Vegetables <dbl>, Confirmed_per_capita <dbl>,
## #   Deaths_per_capita <dbl>, Cases_vs_median <chr>, Deaths_vs_median <chr>

corrplot(is.corr=TRUE, cor(food_data[,2:24], use="pairwise.complete.obs"), method="number")

chart.Correlation(food_data[,2:24], histogram=TRUE)

# summary statistics
food_data_1 <- food_data %>%
  select(-Deaths_vs_median, -Country)
tbl_summary(data = food_data_1, by = "Cases_vs_median",
            statistic = list(all_continuous() ~ "{mean} ({sd})",
                             all_categorical() ~ "{n}({p}%)")) %>%
  add_n() %>%
  add_p(test = all_continuous() ~ "aov") %>%
  as_flex_table() %>%
  bold(part = "header")

Characteristic	N	Above, N = 771	Below, N = 771	p-value2
Alcoholic Beverages	154	1.76 (1.15)	0.86 (0.78)	<0.001
Animal Products	154	11.5 (4.1)	6.6 (4.2)	<0.001
Animal fats	154	1.77 (1.50)	0.76 (0.85)	<0.001
Aquatic Products, Other	154			0.12
0		77(100%)	73(95%)
0.0185		0(0%)	1(1.3%)
0.0209		0(0%)	1(1.3%)
0.0336		0(0%)	1(1.3%)
0.4007		0(0%)	1(1.3%)
Cereals - Excluding Beer	154	18 (5)	23 (7)	<0.001
Eggs	154	0.52 (0.26)	0.32 (0.32)	<0.001
Fish, Seafood	154	0.61 (0.60)	0.57 (0.50)	0.7
Fruits - Excluding Wine	154	2.21 (1.46)	1.80 (1.43)	0.082
Meat	154	4.44 (1.68)	2.93 (2.25)	<0.001
Milk - Excluding Butter	154	3.99 (1.84)	1.89 (1.72)	<0.001
Offals	154	0.15 (0.09)	0.14 (0.13)	0.6
Oilcrops	154	0.66 (0.83)	1.43 (1.85)	0.001
Pulses	154	0.79 (0.73)	1.48 (1.52)	<0.001
Spices	154	0.18 (0.24)	0.19 (0.25)	>0.9
Starchy Roots	154	2.2 (2.4)	4.3 (5.0)	0.001
Stimulants	154	0.46 (0.36)	0.15 (0.16)	<0.001
Sugar Crops	154	0.00 (0.01)	0.04 (0.10)	0.005
Sugar & Sweeteners	154	5.62 (1.63)	3.92 (2.22)	<0.001
Treenuts	154	0.32 (0.29)	0.22 (0.29)	0.035
Vegetal Products	154	38.5 (4.1)	43.4 (4.2)	<0.001
Vegetable Oils	154	5.09 (2.17)	4.66 (2.19)	0.2
Vegetables	154	1.20 (0.63)	0.93 (0.63)	0.008
Confirmed_per_capita	154	161 (282)	1 (2)	<0.001
Deaths_per_capita	154	2.21 (3.74)	0.03 (0.05)	<0.001
1Mean (SD); n(%)
2One-way ANOVA; Fisher's exact test

food_data_2 <- food_data %>%
  select(-Cases_vs_median, -Country)
tbl_summary(data = food_data_2, by = "Deaths_vs_median",
            statistic = list(all_continuous() ~ "{mean} ({sd})",
                             all_categorical() ~ "{n}({p}%)")) %>%
  add_n() %>%
  add_p(test = all_continuous() ~ "aov") %>%
  as_flex_table() %>%
  bold(part = "header")

Characteristic	N	Above, N = 771	Below, N = 771	p-value2
Alcoholic Beverages	154	1.75 (1.15)	0.88 (0.80)	<0.001
Animal Products	154	11.4 (4.2)	6.7 (4.2)	<0.001
Animal fats	154	1.78 (1.50)	0.75 (0.83)	<0.001
Aquatic Products, Other	154			0.12
0		77(100%)	73(95%)
0.0185		0(0%)	1(1.3%)
0.0209		0(0%)	1(1.3%)
0.0336		0(0%)	1(1.3%)
0.4007		0(0%)	1(1.3%)
Cereals - Excluding Beer	154	18 (5)	23 (7)	<0.001
Eggs	154	0.53 (0.26)	0.31 (0.32)	<0.001
Fish, Seafood	154	0.60 (0.60)	0.58 (0.50)	0.8
Fruits - Excluding Wine	154	2.08 (1.37)	1.94 (1.54)	0.5
Meat	154	4.38 (1.74)	2.99 (2.24)	<0.001
Milk - Excluding Butter	154	3.98 (1.84)	1.90 (1.73)	<0.001
Offals	154	0.14 (0.08)	0.14 (0.14)	>0.9
Oilcrops	154	0.68 (0.94)	1.42 (1.81)	0.002
Pulses	154	0.78 (0.68)	1.49 (1.54)	<0.001
Spices	154	0.17 (0.23)	0.20 (0.25)	0.5
Starchy Roots	154	2.0 (2.3)	4.5 (5.0)	<0.001
Stimulants	154	0.46 (0.36)	0.15 (0.17)	<0.001
Sugar Crops	154	0.00 (0.01)	0.04 (0.10)	0.004
Sugar & Sweeteners	154	5.67 (1.65)	3.86 (2.16)	<0.001
Treenuts	154	0.31 (0.28)	0.22 (0.30)	0.045
Vegetal Products	154	38.6 (4.2)	43.3 (4.2)	<0.001
Vegetable Oils	154	5.24 (2.20)	4.52 (2.12)	0.041
Vegetables	154	1.19 (0.64)	0.94 (0.62)	0.013
Confirmed_per_capita	154	157 (283)	5 (27)	<0.001
Deaths_per_capita	154	2.21 (3.74)	0.03 (0.04)	<0.001
1Mean (SD); n(%)
2One-way ANOVA; Fisher's exact test

# prepare data for cross validation
food_data <- food_data %>%
  # delete country since only each country has only one observation
  select(-`Animal Products`, -Country)
food_data %>% head()

## # A tibble: 6 x 25
##   `Alcoholic Beve… `Animal fats` `Aquatic Produc… `Cereals - Excl…   Eggs
##              <dbl>         <dbl>            <dbl>            <dbl>  <dbl>
## 1           0              0.850                0             37.1 0.150 
## 2           0.912          1.06                 0             16.2 0.809 
## 3           0.0896         0.194                0             25.0 0.418 
## 4           1.94           0.264                0             18.4 0.0441
## 5           1.44           1.06                 0             16.8 0.864 
## 6           0.227          1.77                 0             19.3 0.731 
## # … with 20 more variables: `Fish, Seafood` <dbl>, `Fruits - Excluding
## #   Wine` <dbl>, Meat <dbl>, `Milk - Excluding Butter` <dbl>, Offals <dbl>,
## #   Oilcrops <dbl>, Pulses <dbl>, Spices <dbl>, `Starchy Roots` <dbl>,
## #   Stimulants <dbl>, `Sugar Crops` <dbl>, `Sugar & Sweeteners` <dbl>,
## #   Treenuts <dbl>, `Vegetal Products` <dbl>, `Vegetable Oils` <dbl>,
## #   Vegetables <dbl>, Confirmed_per_capita <dbl>, Deaths_per_capita <dbl>,
## #   Cases_vs_median <chr>, Deaths_vs_median <chr>

# numeric 
set.seed(123)
cv_folds_10 = createFolds(y=food_data$Confirmed_per_capita, k=10)
result_lm <- list()
result_knn <- list()
result_lasso <- list()
result_ridge <- list()
      for(f in 1:length(cv_folds_10)){
        food_data_train_cv_10 <- food_data[-cv_folds_10[[f]],]
        food_data_test_cv_10 <- food_data[cv_folds_10[[f]],]
        lm_fit = lm(Confirmed_per_capita~.-Deaths_per_capita-Cases_vs_median-Deaths_vs_median, data = food_data_train_cv_10)
        knn_fit = train(Confirmed_per_capita~.-Deaths_per_capita-Cases_vs_median-Deaths_vs_median, data = food_data_train_cv_10, 
                         method = "knn", tuneLength = 20, preProcess = c("scale", "center"),
                        trControl = trainControl(method="cv", number = 5))
        lasso_fit = cv.glmnet(x = data.matrix(food_data[,c(1:21)]), y = data.matrix(food_data[,22]), alpha=1)
        ridge_fit = cv.glmnet(x = data.matrix(food_data[,c(1:21)]), y = data.matrix(food_data[,22]), alpha=0)
        
        #linear
        food_data_test_cv_10$Confirmed_lm_predict <- predict(lm_fit, newdata = food_data_test_cv_10)
        result_lm[[f]] = mean((food_data_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_lm_predict)^2, na.rm=TRUE)
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_lm_predict)
        #knn
        food_data_test_cv_10$Confirmed_knn_predict <- predict(knn_fit, newdata = food_data_test_cv_10)
        result_knn[[f]] = mean((food_data_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_knn_predict)^2, na.rm=TRUE)
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_knn_predict)
        #lasso
        food_data_test_cv_10 = as.data.frame(food_data_test_cv_10)
        food_data_test_cv_10$Confirmed_lasso_predict <- as.matrix(cbind(1,food_data_test_cv_10[,c(1:21)])) %*% coef(lasso_fit, s = "lambda.min")
        result_lasso[[f]] = mean((food_data_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_lasso_predict)^2, na.rm=TRUE)
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_lasso_predict)        
        #ridge
        food_data_test_cv_10$Confirmed_ridge_predict <- as.matrix(cbind(1,food_data_test_cv_10[,c(1:21)])) %*% coef(ridge_fit, s = "lambda.min")
        result_ridge[[f]] = mean((food_data_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_ridge_predict)^2, na.rm=TRUE)
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_ridge_predict)
      }

data.frame_lm = data.frame("CV_error" = mean(unlist(result_lm)), "CV_error_SE" = sd(unlist(result_lm)))
data.frame_knn = data.frame("CV_error" = mean(unlist(result_knn)), "CV_error_SE" = sd(unlist(result_knn)))
data.frame_lasso = data.frame("CV_error" = mean(unlist(result_lasso)), "CV_error_SE" = sd(unlist(result_lasso)))
data.frame_ridge = data.frame("CV_error" = mean(unlist(result_ridge)), "CV_error_SE" = sd(unlist(result_ridge)))
rbind("Linear Regression" = data.frame_lm, "KNN" = data.frame_knn, "Lasso" = data.frame_lasso, "Ridge" = data.frame_ridge)

##                   CV_error CV_error_SE
## Linear Regression 61949.59    83274.45
## KNN               38668.35    43959.12
## Lasso             26944.69    29722.09
## Ridge             34409.81    40599.06

# categorical
set.seed(123)
cv_folds_10 = createFolds(y=food_data$Cases_vs_median, k=10)
result_logistic <- list()
result_knn <- list()
result_linear_svm <- list()
result_radial_svm <- list()
result_polynomial_svm <- list()
food_data %>% head()

## # A tibble: 6 x 25
##   `Alcoholic Beve… `Animal fats` `Aquatic Produc… `Cereals - Excl…   Eggs
##              <dbl>         <dbl>            <dbl>            <dbl>  <dbl>
## 1           0              0.850                0             37.1 0.150 
## 2           0.912          1.06                 0             16.2 0.809 
## 3           0.0896         0.194                0             25.0 0.418 
## 4           1.94           0.264                0             18.4 0.0441
## 5           1.44           1.06                 0             16.8 0.864 
## 6           0.227          1.77                 0             19.3 0.731 
## # … with 20 more variables: `Fish, Seafood` <dbl>, `Fruits - Excluding
## #   Wine` <dbl>, Meat <dbl>, `Milk - Excluding Butter` <dbl>, Offals <dbl>,
## #   Oilcrops <dbl>, Pulses <dbl>, Spices <dbl>, `Starchy Roots` <dbl>,
## #   Stimulants <dbl>, `Sugar Crops` <dbl>, `Sugar & Sweeteners` <dbl>,
## #   Treenuts <dbl>, `Vegetal Products` <dbl>, `Vegetable Oils` <dbl>,
## #   Vegetables <dbl>, Confirmed_per_capita <dbl>, Deaths_per_capita <dbl>,
## #   Cases_vs_median <chr>, Deaths_vs_median <chr>

food_data <- food_data %>%
  mutate(Cases_vs_median = as.factor(ifelse(Cases_vs_median == "Above",1,0)),
         Deaths_vs_median = as.factor(ifelse(Deaths_vs_median == "Above",1,0)))

      for(f in 1:length(cv_folds_10)){
        food_data_train_cv_10 <- food_data[-cv_folds_10[[f]],]
        food_data_test_cv_10 <- food_data[cv_folds_10[[f]],]
        knn_fit <- train(Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, 
                         method = "knn", tuneLength = 20, preProcess = c("scale", "center"),
                        trControl = trainControl(method="cv", number = 5))
        logistic_fit <- glm(Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, family = binomial())
        svr_linear_tune <- tune(svm, Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, kernel ="linear")
        linear_svm_fit <- svr_linear_tune$best.model
        svr_radial_tune <- tune(svm, Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, kernel ="radial")
        radial_svm_fit <- svr_radial_tune$best.model
        svr_polynomial_tune <- tune(svm, Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, kernel ="polynomial")
        polynomial_svm_fit <- svr_polynomial_tune$best.model

        # knn
        food_data_test_cv_10$Confirmed_knn_predict <- predict(knn_fit, newdata = food_data_test_cv_10)
        result_knn[[f]] <- 1-confusionMatrix(data = food_data_test_cv_10$Confirmed_knn_predict, reference = as.factor(food_data_test_cv_10$Cases_vs_median))$overall[1]
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_knn_predict)
        #logistic
        food_data_test_cv_10$Confirmed_logistic_predict_num <- predict(logistic_fit, newdata = food_data_test_cv_10, type="response", na.action=na.exclude)
        food_data_test_cv_10$Confirmed_logistic_predict <- as_factor(ifelse(food_data_test_cv_10$Confirmed_logistic_predict_num >= 0.5, 1, 0))
        result_logistic[[f]] <- 1- confusionMatrix(data = food_data_test_cv_10$Confirmed_logistic_predict, reference = as.factor(food_data_test_cv_10$Cases_vs_median))$overall[1]
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_logistic_predict, -Confirmed_logistic_predict_num )
        # linear svm
        food_data_test_cv_10$Confirmed_linear_svm_predict <- predict(linear_svm_fit, newdata = food_data_test_cv_10)
        result_linear_svm[[f]] <- 1- confusionMatrix(data = food_data_test_cv_10$Confirmed_linear_svm_predict, reference = as.factor(food_data_test_cv_10$Cases_vs_median))$overall[1]
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_linear_svm_predict)
        # radial svm
        food_data_test_cv_10$Confirmed_radial_svm_predict <- predict(radial_svm_fit, newdata = food_data_test_cv_10)
        result_radial_svm[[f]] <- 1- confusionMatrix(data = food_data_test_cv_10$Confirmed_radial_svm_predict, reference = as.factor(food_data_test_cv_10$Cases_vs_median))$overall[1]
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_radial_svm_predict)
        # polynomial svm
        food_data_test_cv_10$Confirmed_polynomial_svm_predict <- predict(polynomial_svm_fit, newdata = food_data_test_cv_10)
        result_polynomial_svm[[f]] <- 1- confusionMatrix(data = food_data_test_cv_10$Confirmed_polynomial_svm_predict, reference = as.factor(food_data_test_cv_10$Cases_vs_median))$overall[1]
        food_data_test_cv_10 <- food_data_test_cv_10 %>%
          select(-Confirmed_polynomial_svm_predict)
      }

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

## Warning: glm.fit: fitted probabilities numerically 0 or 1 occurred

data.frame_knn = data.frame("CV_error" = mean(unlist(result_knn)), "CV_error_SE" = sd(unlist(result_knn)))
data.frame_logistic = data.frame("CV_error" = mean(unlist(result_logistic)), "CV_error_SE" = sd(unlist(result_logistic)))
data.frame_linear_svm = data.frame("CV_error" = mean(unlist(result_linear_svm)), "CV_error_SE" = sd(unlist(result_linear_svm)))
data.frame_radial_svm = data.frame("CV_error" = mean(unlist(result_radial_svm)), "CV_error_SE" = sd(unlist(result_radial_svm)))
data.frame_polynomial_svm = data.frame("CV_error" = mean(unlist(result_polynomial_svm)), "CV_error_SE" = sd(unlist(result_polynomial_svm)))

rbind("KNN" = data.frame_knn, "Logistic Regression" = data.frame_logistic, "Linear SVM" = data.frame_linear_svm, "Radial SVM" = data.frame_radial_svm, "Polynomial SVM" = data.frame_polynomial_svm)

##                      CV_error CV_error_SE
## KNN                 0.2301190  0.09472007
## Logistic Regression 0.2154167  0.08665864
## Linear SVM          0.2016667  0.08239447
## Radial SVM          0.2417857  0.07898161
## Polynomial SVM      0.2536905  0.08373853

    lasso_fit = cv.glmnet(x = data.matrix(food_data[,c(1:21)]), y = data.matrix(food_data[,24]), alpha=1)
    ridge_fit = cv.glmnet(x = data.matrix(food_data[,c(1:21)]), y = data.matrix(food_data[,24]), alpha=0)

qda_fit = train(Cases_vs_median~.-Confirmed_per_capita -Deaths_per_capita -Deaths_vs_median, data = food_data_train_cv_10, method = “qda”)

    #lasso
    food_data_test_cv_10 = as.data.frame(food_data_test_cv_10)
    food_data_test_cv_10$Confirmed_lasso_predict <- as.matrix(cbind(1,food_data_test_cv_10[,c(1:21)])) %*% coef(lasso_fit, s = "lambda.min")
    result_lasso[[f]] = mean((food_data_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_lasso_predict)^2, na.rm=TRUE)
    food_data_test_cv_10 <- food_data_test_cv_10 %>%
      select(-Confirmed_lasso_predict)
    #ridge
    food_data_test_cv_10$Confirmed_ridge_predict <- as.matrix(cbind(1,food_data_test_cv_10[,c(1:21)])) %*% coef(ridge_fit, s = "lambda.min")
    result_ridge[[f]] = mean((kcal_test_cv_10$Confirmed_per_capita - food_data_test_cv_10$Confirmed_ridge_predict)^2, na.rm=TRUE)
    food_data_test_cv_10 <- food_data_test_cv_10 %>%
      select(-Confirmed_ridge_predict)

data.frame_lasso = data.frame(“CV_error” = mean(unlist(result_lasso)), “CV_error_SE” = sd(unlist(result_lasso))) data.frame_ridge = data.frame(“CV_error” = mean(unlist(result_ridge)), “CV_error_SE” = sd(unlist(result_ridge)))

635FinalProject

Zhitong Yu

4/23/2021